LMFDB - Embedded newform 54.21.d.a.35.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [54,21,Mod(17,54)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("54.17"); S:= CuspForms(chi, 21); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(54, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 21, names="a")

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 21 $
Character orbit:	$[\chi]$	$=$	54.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$136.897433155$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			35.16
Character	$\chi$	$=$	54.35
Dual form			54.21.d.a.17.16

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(627.069 + 362.039i) q^{2} +(262144. + 454047. i) q^{4} +(5.93247e6 - 3.42511e6i) q^{5} +(1.73104e8 - 2.99825e8i) q^{7} +3.79625e8i q^{8} +4.96010e9 q^{10} +(3.11848e10 + 1.80045e10i) q^{11} +(-5.45632e10 - 9.45063e10i) q^{13} +(2.17097e11 - 1.25341e11i) q^{14} +(-1.37439e11 + 2.38051e11i) q^{16} -3.94900e12i q^{17} -6.76417e11 q^{19} +(3.11032e12 + 1.79575e12i) q^{20} +(1.30367e13 + 2.25802e13i) q^{22} +(3.84169e13 - 2.21800e13i) q^{23} +(-2.42209e13 + 4.19518e13i) q^{25} -7.90160e13i q^{26} +1.81513e14 q^{28} +(4.23142e14 + 2.44301e14i) q^{29} +(-1.45353e14 - 2.51760e14i) q^{31} +(-1.72368e14 + 9.95164e13i) q^{32} +(1.42969e15 - 2.47629e15i) q^{34} -2.37161e15i q^{35} -3.69514e15 q^{37} +(-4.24161e14 - 2.44889e14i) q^{38} +(1.30026e15 + 2.25212e15i) q^{40} +(-9.98071e15 + 5.76237e15i) q^{41} +(1.08739e16 - 1.88342e16i) q^{43} +1.88791e16i q^{44} +3.21201e16 q^{46} +(-5.92624e16 - 3.42152e16i) q^{47} +(-2.00339e16 - 3.46998e16i) q^{49} +(-3.03764e16 + 1.75378e16i) q^{50} +(2.86069e16 - 4.95485e16i) q^{52} -1.35148e17i q^{53} +2.46670e17 q^{55} +(1.13821e17 + 6.57146e16i) q^{56} +(1.76893e17 + 3.06387e17i) q^{58} +(-6.48610e17 + 3.74475e17i) q^{59} +(-2.20266e17 + 3.81512e17i) q^{61} -2.10494e17i q^{62} -1.44115e17 q^{64} +(-6.47390e17 - 3.73771e17i) q^{65} +(-1.65980e18 - 2.87486e18i) q^{67} +(1.79303e18 - 1.03521e18i) q^{68} +(8.58613e17 - 1.48716e18i) q^{70} +3.20903e18i q^{71} +7.00433e18 q^{73} +(-2.31711e18 - 1.33778e18i) q^{74} +(-1.77319e17 - 3.07125e17i) q^{76} +(1.07964e19 - 6.23332e18i) q^{77} +(-2.66102e18 + 4.60903e18i) q^{79} +1.88298e18i q^{80} -8.34480e18 q^{82} +(-3.82852e18 - 2.21040e18i) q^{83} +(-1.35258e19 - 2.34273e19i) q^{85} +(1.36374e19 - 7.87355e18i) q^{86} +(-6.83497e18 + 1.18385e19i) q^{88} -5.02252e19i q^{89} -3.77805e19 q^{91} +(2.01415e19 + 1.16287e19i) q^{92} +(-2.47744e19 - 4.29105e19i) q^{94} +(-4.01283e18 + 2.31681e18i) q^{95} +(5.30109e18 - 9.18176e18i) q^{97} -2.90122e19i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10485760 q^{4} - 29763918 q^{5} + 133479866 q^{7} + 35793208728 q^{11} + 39827158550 q^{13} - 187564400640 q^{14} - 5497558138880 q^{16} - 10560819523540 q^{19} - 15604865040384 q^{20} + 10829007458304 q^{22}+ \cdots - 66\!\cdots\!16 q^{97}+O(q^{100}) $ 40 * q + 10485760 * q^4 - 29763918 * q^5 + 133479866 * q^7 + 35793208728 * q^11 + 39827158550 * q^13 - 187564400640 * q^14 - 5497558138880 * q^16 - 10560819523540 * q^19 - 15604865040384 * q^20 + 10829007458304 * q^22 + 95164852839678 * q^23 + 485893942617694 * q^25 + 139963783970816 * q^28 - 487337329131246 * q^29 - 386065992062842 * q^31 - 810410730184704 * q^34 + 7650497672534432 * q^37 + 27431157167935488 * q^38 + 76546903885431012 * q^41 - 10868849409851092 * q^43 + 13732137981788160 * q^46 - 220882065588142506 * q^47 - 201918836583922386 * q^49 - 84434006357065728 * q^50 - 20880901301862400 * q^52 - 689556443803109316 * q^55 - 98337764482744320 * q^56 + 289875600503808000 * q^58 + 4671324023815652220 * q^59 - 608513692992272866 * q^61 - 5764607523034234880 * q^64 - 4959300225343873626 * q^65 - 2581864509390888904 * q^67 + 5171455594224156672 * q^68 - 584784912675889152 * q^70 + 15022099327729072004 * q^73 - 7089371473773993984 * q^74 - 2768455473178869760 * q^76 + 30865724759591472834 * q^77 + 18532232803602736754 * q^79 - 35601230743051272192 * q^82 - 54829678294093455594 * q^83 + 43688870161052471388 * q^85 - 47393791396458614784 * q^86 - 5677518662299287552 * q^88 - 35182774173576758996 * q^91 + 49893790365609099264 * q^92 + 19892618446780047360 * q^94 - 332020921293200455200 * q^95 - 66463398176406835216 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	627.069	+	362.039i	0.612372	+	0.353553i
$2$	627.069	+	362.039i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	262144.	+	454047.i	0.250000	+	0.433013i
$5$	5.93247e6	−	3.42511e6i	0.607485	−	0.350732i	−0.164495	−	0.986378i	$-0.552600\pi$
$5$	5.93247e6	−	3.42511e6i	0.607485	−	0.350732i	0.771981	+	0.635646i	$0.219266\pi$
$6$		0			0
$7$	1.73104e8	−	2.99825e8i	0.612812	−	1.06142i	−0.377953	−	0.925825i	$-0.623372\pi$
$7$	1.73104e8	−	2.99825e8i	0.612812	−	1.06142i	0.990764	−	0.135596i	$-0.0432948\pi$
$8$			3.79625e8i			0.353553i
$9$		0			0
$10$	4.96010e9			0.496010
$11$	3.11848e10	+	1.80045e10i	1.20231	+	0.694153i	0.961068	−	0.276313i	$-0.0891125\pi$
$11$	3.11848e10	+	1.80045e10i	1.20231	+	0.694153i	0.241240	+	0.970465i	$0.422446\pi$
$12$		0			0
$13$	−5.45632e10	−	9.45063e10i	−0.395792	−	0.685531i	0.597410	−	0.801936i	$-0.296196\pi$
$13$	−5.45632e10	−	9.45063e10i	−0.395792	−	0.685531i	−0.993202	+	0.116405i	$0.962863\pi$
$14$	2.17097e11	−	1.25341e11i	0.750538	−	0.433323i
$15$		0			0
$16$	−1.37439e11	+	2.38051e11i	−0.125000	+	0.216506i
$17$		−	3.94900e12i		−	1.95883i	−0.201849	−	0.979417i	$-0.564695\pi$
$17$		−	3.94900e12i		−	1.95883i	0.201849	−	0.979417i	$-0.435305\pi$
$18$		0			0
$19$	−6.76417e11			−0.110326			−0.0551631	−	0.998477i	$-0.517568\pi$
$19$	−6.76417e11			−0.110326			−0.0551631	+	0.998477i	$0.517568\pi$
$20$	3.11032e12	+	1.79575e12i	0.303743	+	0.175366i
$21$		0			0
$22$	1.30367e13	+	2.25802e13i	0.490840	+	0.850160i
$23$	3.84169e13	−	2.21800e13i	0.927351	−	0.535406i	0.0413781	−	0.999144i	$-0.486825\pi$
$23$	3.84169e13	−	2.21800e13i	0.927351	−	0.535406i	0.885973	+	0.463737i	$0.153492\pi$
$24$		0			0
$25$	−2.42209e13	+	4.19518e13i	−0.253975	+	0.439897i
$26$		−	7.90160e13i		−	0.559734i
$27$		0			0
$28$	1.81513e14			0.612812
$29$	4.23142e14	+	2.44301e14i	1.00579	+	0.580691i	0.909955	−	0.414707i	$-0.136116\pi$
$29$	4.23142e14	+	2.44301e14i	1.00579	+	0.580691i	0.0958311	+	0.995398i	$0.469449\pi$
$30$		0			0
$31$	−1.45353e14	−	2.51760e14i	−0.177341	−	0.307163i	0.763628	−	0.645656i	$-0.223416\pi$
$31$	−1.45353e14	−	2.51760e14i	−0.177341	−	0.307163i	−0.940969	+	0.338493i	$0.890083\pi$
$32$	−1.72368e14	+	9.95164e13i	−0.153093	+	0.0883883i
$33$		0			0
$34$	1.42969e15	−	2.47629e15i	0.692552	−	1.19954i
$35$		−	2.37161e15i		−	0.859730i
$36$		0			0
$37$	−3.69514e15			−0.768447			−0.384223	−	0.923240i	$-0.625531\pi$
$37$	−3.69514e15			−0.768447			−0.384223	+	0.923240i	$0.625531\pi$
$38$	−4.24161e14	−	2.44889e14i	−0.0675607	−	0.0390062i
$39$		0			0
$40$	1.30026e15	+	2.25212e15i	0.124002	+	0.214778i
$41$	−9.98071e15	+	5.76237e15i	−0.743572	+	0.429301i	−0.823367	−	0.567510i	$-0.807907\pi$
$41$	−9.98071e15	+	5.76237e15i	−0.743572	+	0.429301i	0.0797946	+	0.996811i	$0.474574\pi$
$42$		0			0
$43$	1.08739e16	−	1.88342e16i	0.503154	−	0.871489i	−0.496839	−	0.867843i	$-0.665506\pi$
$43$	1.08739e16	−	1.88342e16i	0.503154	−	0.871489i	0.999993	−	0.00364595i	$-0.00116054\pi$
$44$			1.88791e16i			0.694153i
$45$		0			0
$46$	3.21201e16			0.757179
$47$	−5.92624e16	−	3.42152e16i	−1.12668	−	0.650489i	−0.183582	−	0.983004i	$-0.558769\pi$
$47$	−5.92624e16	−	3.42152e16i	−1.12668	−	0.650489i	−0.943098	+	0.332516i	$0.892103\pi$
$48$		0			0
$49$	−2.00339e16	−	3.46998e16i	−0.251076	−	0.434876i
$50$	−3.03764e16	+	1.75378e16i	−0.311054	+	0.179587i
$51$		0			0
$52$	2.86069e16	−	4.95485e16i	0.197896	−	0.342766i
$53$		−	1.35148e17i		−	0.772771i	−0.922337	−	0.386386i	$-0.873723\pi$
$53$		−	1.35148e17i		−	0.772771i	0.922337	−	0.386386i	$-0.126277\pi$
$54$		0			0
$55$	2.46670e17			0.973846
$56$	1.13821e17	+	6.57146e16i	0.375269	+	0.216662i
$57$		0			0
$58$	1.76893e17	+	3.06387e17i	0.410611	+	0.711198i
$59$	−6.48610e17	+	3.74475e17i	−1.26901	+	0.732661i	−0.974800	−	0.223081i	$-0.928388\pi$
$59$	−6.48610e17	+	3.74475e17i	−1.26901	+	0.732661i	−0.294206	+	0.955742i	$0.595055\pi$
$60$		0			0
$61$	−2.20266e17	+	3.81512e17i	−0.308780	+	0.534823i	−0.978096	−	0.208155i	$-0.933254\pi$
$61$	−2.20266e17	+	3.81512e17i	−0.308780	+	0.534823i	0.669316	+	0.742978i	$0.266587\pi$
$62$		−	2.10494e17i		−	0.250798i
$63$		0			0
$64$	−1.44115e17			−0.125000
$65$	−6.47390e17	−	3.73771e17i	−0.480875	−	0.277633i
$66$		0			0
$67$	−1.65980e18	−	2.87486e18i	−0.910558	−	1.57713i	−0.813278	−	0.581875i	$-0.802319\pi$
$67$	−1.65980e18	−	2.87486e18i	−0.910558	−	1.57713i	−0.0972793	−	0.995257i	$-0.531014\pi$
$68$	1.79303e18	−	1.03521e18i	0.848200	−	0.489708i
$69$		0			0
$70$	8.58613e17	−	1.48716e18i	0.303960	−	0.526475i
$71$			3.20903e18i			0.985805i	0.870085	+	0.492902i	$0.164064\pi$
$71$			3.20903e18i			0.985805i	−0.870085	+	0.492902i	$0.835936\pi$
$72$		0			0
$73$	7.00433e18			1.62981			0.814906	−	0.579593i	$-0.196788\pi$
$73$	7.00433e18			1.62981			0.814906	+	0.579593i	$0.196788\pi$
$74$	−2.31711e18	−	1.33778e18i	−0.470576	−	0.271687i
$75$		0			0
$76$	−1.77319e17	−	3.07125e17i	−0.0275816	−	0.0477727i
$77$	1.07964e19	−	6.23332e18i	1.47358	−	0.850770i
$78$		0			0
$79$	−2.66102e18	+	4.60903e18i	−0.281046	+	0.486786i	−0.971643	−	0.236454i	$-0.924015\pi$
$79$	−2.66102e18	+	4.60903e18i	−0.281046	+	0.486786i	0.690596	+	0.723240i	$0.257348\pi$
$80$			1.88298e18i			0.175366i
$81$		0			0
$82$	−8.34480e18			−0.607124
$83$	−3.82852e18	−	2.21040e18i	−0.246746	−	0.142459i	0.371527	−	0.928422i	$-0.378834\pi$
$83$	−3.82852e18	−	2.21040e18i	−0.246746	−	0.142459i	−0.618273	+	0.785963i	$0.712168\pi$
$84$		0			0
$85$	−1.35258e19	−	2.34273e19i	−0.687025	−	1.18996i
$86$	1.36374e19	−	7.87355e18i	0.616235	−	0.355784i
$87$		0			0
$88$	−6.83497e18	+	1.18385e19i	−0.245420	+	0.425080i
$89$		−	5.02252e19i		−	1.61073i	−0.592783	−	0.805363i	$-0.701971\pi$
$89$		−	5.02252e19i		−	1.61073i	0.592783	−	0.805363i	$-0.298029\pi$
$90$		0			0
$91$	−3.77805e19			−0.970183
$92$	2.01415e19	+	1.16287e19i	0.463675	+	0.267703i
$93$		0			0
$94$	−2.47744e19	−	4.29105e19i	−0.459965	−	0.796683i
$95$	−4.01283e18	+	2.31681e18i	−0.0670216	+	0.0386949i
$96$		0			0
$97$	5.30109e18	−	9.18176e18i	0.0718866	−	0.124511i	−0.827842	−	0.560962i	$-0.810431\pi$
$97$	5.30109e18	−	9.18176e18i	0.0718866	−	0.124511i	0.899728	+	0.436451i	$0.143765\pi$
$98$		−	2.90122e19i		−	0.355075i
$99$		0			0
$100$	−2.53975e19			−0.253975
$101$	−1.36492e19	−	7.88038e18i	−0.123565	−	0.0713400i	0.436944	−	0.899489i	$-0.356061\pi$
$101$	−1.36492e19	−	7.88038e18i	−0.123565	−	0.0713400i	−0.560508	+	0.828149i	$0.689394\pi$
$102$		0			0
$103$	1.30666e19	+	2.26319e19i	0.0972274	+	0.168403i	0.910536	−	0.413430i	$-0.135669\pi$
$103$	1.30666e19	+	2.26319e19i	0.0972274	+	0.168403i	−0.813309	+	0.581833i	$0.802336\pi$
$104$	3.58770e19	−	2.07136e19i	0.242372	−	0.139933i
$105$		0			0
$106$	4.89288e19	−	8.47472e19i	0.273216	−	0.473224i
$107$			4.16493e18i			0.0211724i	0.999944	+	0.0105862i	$0.00336975\pi$
$107$			4.16493e18i			0.0211724i	−0.999944	+	0.0105862i	$0.996630\pi$
$108$		0			0
$109$	4.08736e20			1.72654			0.863272	−	0.504739i	$-0.168411\pi$
$109$	4.08736e20			1.72654			0.863272	+	0.504739i	$0.168411\pi$
$110$	1.54679e20	+	8.93042e19i	0.596356	+	0.344306i
$111$		0			0
$112$	4.75825e19	+	8.24153e19i	0.153203	+	0.265355i
$113$	3.28419e20	−	1.89613e20i	0.967483	−	0.558577i	0.0690151	−	0.997616i	$-0.478014\pi$
$113$	3.28419e20	−	1.89613e20i	0.967483	−	0.558577i	0.898468	+	0.439039i	$0.144681\pi$
$114$		0			0
$115$	1.51938e20	−	2.63165e20i	0.375568	−	0.650503i
$116$			2.56168e20i			0.580691i
$117$		0			0
$118$	−5.42298e20			−1.03614
$119$	−1.18401e21	−	6.83587e20i	−2.07915	−	1.20040i
$120$		0			0
$121$	3.11952e20	+	5.40316e20i	0.463696	+	0.803146i
$122$	−2.76244e20	+	1.59490e20i	−0.378177	+	0.218340i
$123$		0			0
$124$	7.62071e19	−	1.31995e20i	0.0886703	−	0.153582i
$125$			9.85126e20i			1.05777i
$126$		0			0
$127$	1.42207e21			1.30282			0.651409	−	0.758727i	$-0.274178\pi$
$127$	1.42207e21			1.30282			0.651409	+	0.758727i	$0.274178\pi$
$128$	−9.03702e19	−	5.21753e19i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−2.70639e20	−	4.68760e20i	−0.196316	−	0.340030i
$131$	−1.01421e21	+	5.85556e20i	−0.681422	+	0.393419i	−0.800391	−	0.599479i	$-0.795375\pi$
$131$	−1.01421e21	+	5.85556e20i	−0.681422	+	0.393419i	0.118968	+	0.992898i	$0.462041\pi$
$132$		0			0
$133$	−1.17091e20	+	2.02807e20i	−0.0676092	+	0.117103i
$134$		−	2.40365e21i		−	1.28772i
$135$		0			0
$136$	1.49914e21			0.692552
$137$	−3.19830e20	−	1.84654e20i	−0.137314	−	0.0792780i	0.429770	−	0.902939i	$-0.358595\pi$
$137$	−3.19830e20	−	1.84654e20i	−0.137314	−	0.0792780i	−0.567083	+	0.823661i	$0.691928\pi$
$138$		0			0
$139$	2.33978e20	+	4.05262e20i	0.0869015	+	0.150518i	0.906200	−	0.422850i	$-0.138970\pi$
$139$	2.33978e20	+	4.05262e20i	0.0869015	+	0.150518i	−0.819298	+	0.573367i	$0.805637\pi$
$140$	1.07682e21	−	6.21702e20i	0.372274	−	0.214932i
$141$		0			0
$142$	−1.16179e21	+	2.01229e21i	−0.348535	+	0.603680i
$143$		−	3.92954e21i		−	1.09896i
$144$		0			0
$145$	3.34703e21			0.814667
$146$	4.39220e21	+	2.53584e21i	0.998052	+	0.576226i
$147$		0			0
$148$	−9.68659e20	−	1.67777e21i	−0.192112	−	0.332747i
$149$	2.52379e21	−	1.45711e21i	0.467941	−	0.270166i	−0.247436	−	0.968904i	$-0.579588\pi$
$149$	2.52379e21	−	1.45711e21i	0.467941	−	0.270166i	0.715377	+	0.698738i	$0.246255\pi$
$150$		0			0
$151$	2.76043e21	−	4.78121e21i	0.447927	−	0.775832i	−0.550324	−	0.834951i	$-0.685496\pi$
$151$	2.76043e21	−	4.78121e21i	0.447927	−	0.775832i	0.998251	+	0.0591188i	$0.0188291\pi$
$152$		−	2.56785e20i		−	0.0390062i
$153$		0			0
$154$	9.02681e21			1.20317
$155$	−1.72461e21	−	9.95704e20i	−0.215464	−	0.124398i
$156$		0			0
$157$	−2.92244e21	−	5.06181e21i	−0.321180	−	0.556300i	0.659552	−	0.751659i	$-0.270746\pi$
$157$	−2.92244e21	−	5.06181e21i	−0.321180	−	0.556300i	−0.980732	+	0.195359i	$0.937413\pi$
$158$	−3.33729e21	+	1.92679e21i	−0.344210	+	0.198730i
$159$		0			0
$160$	−6.81710e20	+	1.18076e21i	−0.0620012	+	0.107389i
$161$		−	1.53578e22i		−	1.31241i
$162$		0			0
$163$	−4.90496e21			−0.370476			−0.185238	−	0.982694i	$-0.559306\pi$
$163$	−4.90496e21			−0.370476			−0.185238	+	0.982694i	$0.559306\pi$
$164$	−5.23277e21	−	3.02114e21i	−0.371786	−	0.214651i
$165$		0			0
$166$	−1.60050e21	−	2.77214e21i	−0.100734	−	0.174476i
$167$	2.41465e22	−	1.39410e22i	1.43117	−	0.826285i	0.433957	−	0.900934i	$-0.357117\pi$
$167$	2.41465e22	−	1.39410e22i	1.43117	−	0.826285i	0.997210	+	0.0746491i	$0.0237837\pi$
$168$		0			0
$169$	3.54819e21	−	6.14564e21i	0.186698	−	0.323370i
$170$		−	1.95874e22i		−	0.971600i
$171$		0			0
$172$	1.14021e22			0.503154
$173$	1.52348e21	+	8.79580e20i	0.0634417	+	0.0366281i	0.531385	−	0.847130i	$-0.321672\pi$
$173$	1.52348e21	+	8.79580e20i	0.0634417	+	0.0366281i	−0.467944	+	0.883758i	$0.655005\pi$
$174$		0			0
$175$	8.38547e21	+	1.45241e22i	0.311277	+	0.539148i
$176$	−8.57201e21	+	4.94905e21i	−0.300577	+	0.173538i
$177$		0			0
$178$	1.81835e22	−	3.14947e22i	0.569477	−	0.986364i
$179$		−	4.92623e22i		−	1.45876i	−0.684107	−	0.729381i	$-0.739808\pi$
$179$		−	4.92623e22i		−	1.45876i	0.684107	−	0.729381i	$-0.260192\pi$
$180$		0			0
$181$	5.28544e22			1.40054			0.700269	−	0.713879i	$-0.253063\pi$
$181$	5.28544e22			1.40054			0.700269	+	0.713879i	$0.253063\pi$
$182$	−2.36910e22	−	1.36780e22i	−0.594113	−	0.343011i
$183$		0			0
$184$	8.42009e21	+	1.45840e22i	0.189295	+	0.327868i
$185$	−2.19213e22	+	1.26563e22i	−0.466820	+	0.269519i
$186$		0			0
$187$	7.10998e22	−	1.23149e23i	1.35973	−	2.35512i
$188$		−	3.58772e22i		−	0.650489i
$189$		0			0
$190$	−3.35510e21			−0.0547229
$191$	−1.99516e22	−	1.15191e22i	−0.308777	−	0.178272i	0.337602	−	0.941289i	$-0.390384\pi$
$191$	−1.99516e22	−	1.15191e22i	−0.308777	−	0.178272i	−0.646379	+	0.763016i	$0.723718\pi$
$192$		0			0
$193$	−2.10837e22	−	3.65180e22i	−0.294017	−	0.509253i	0.680738	−	0.732527i	$-0.261659\pi$
$193$	−2.10837e22	−	3.65180e22i	−0.294017	−	0.509253i	−0.974756	+	0.223273i	$0.928326\pi$
$194$	6.64831e21	−	3.83840e21i	0.0880428	−	0.0508315i
$195$		0			0
$196$	1.05035e22	−	1.81927e22i	0.125538	−	0.217438i
$197$		−	3.67083e22i		−	0.416967i	−0.978026	−	0.208484i	$-0.933147\pi$
$197$		−	3.67083e22i		−	0.416967i	0.978026	−	0.208484i	$-0.0668528\pi$
$198$		0			0
$199$	−1.22128e22			−0.125396			−0.0626981	−	0.998033i	$-0.519971\pi$
$199$	−1.22128e22			−0.125396			−0.0626981	+	0.998033i	$0.519971\pi$
$200$	−1.59260e22	−	9.19486e21i	−0.155527	−	0.0897936i
$201$		0			0
$202$	−5.70600e21	−	9.88309e21i	−0.0504450	−	0.0873733i
$203$	1.46495e23	−	8.45790e22i	1.23271	−	0.711708i
$204$		0			0
$205$	−3.94735e22	+	6.83702e22i	−0.301139	+	0.521589i
$206$			1.89224e22i			0.137500i
$207$		0			0
$208$	2.99965e22			0.197896
$209$	−2.10939e22	−	1.21786e22i	−0.132646	−	0.0765833i
$210$		0			0
$211$	5.65451e22	+	9.79390e22i	0.323274	+	0.559927i	0.981161	−	0.193189i	$-0.0618832\pi$
$211$	5.65451e22	+	9.79390e22i	0.323274	+	0.559927i	−0.657888	+	0.753116i	$0.728550\pi$
$212$	6.13635e22	−	3.54282e22i	0.334620	−	0.193193i
$213$		0			0
$214$	−1.50787e21	+	2.61170e21i	−0.00748557	+	0.0129654i
$215$		−	1.48978e23i		−	0.705889i
$216$		0			0
$217$	−1.00645e23			−0.434706
$218$	2.56306e23	+	1.47978e23i	1.05729	+	0.610426i
$219$		0			0
$220$	6.46632e22	+	1.12000e23i	0.243461	+	0.421688i
$221$	−3.73205e23	+	2.15470e23i	−1.34284	+	0.775290i
$222$		0			0
$223$	−9.42925e22	+	1.63319e23i	−0.310048	+	0.537019i	−0.978372	−	0.206851i	$-0.933678\pi$
$223$	−9.42925e22	+	1.63319e23i	−0.310048	+	0.537019i	0.668325	+	0.743870i	$0.267012\pi$
$224$			6.89068e22i			0.216662i
$225$		0			0
$226$	2.74588e23			0.789947
$227$	1.67797e23	+	9.68775e22i	0.461875	+	0.266664i	0.712832	−	0.701334i	$-0.247412\pi$
$227$	1.67797e23	+	9.68775e22i	0.461875	+	0.266664i	−0.250957	+	0.967998i	$0.580745\pi$
$228$		0			0
$229$	2.37772e23	+	4.11833e23i	0.599523	+	1.03841i	0.992891	+	0.119024i	$0.0379765\pi$
$229$	2.37772e23	+	4.11833e23i	0.599523	+	1.03841i	−0.393368	+	0.919381i	$0.628690\pi$
$230$	1.90552e23	−	1.10015e23i	0.459975	−	0.265567i
$231$		0			0
$232$	−9.27427e22	+	1.60635e23i	−0.205305	+	0.355599i
$233$			1.31657e23i			0.279180i	0.990209	+	0.139590i	$0.0445785\pi$
$233$			1.31657e23i			0.279180i	−0.990209	+	0.139590i	$0.955421\pi$
$234$		0			0
$235$	−4.68763e23			−0.912588
$236$	−3.40058e23	−	1.96333e23i	−0.634503	−	0.366330i
$237$		0			0
$238$	−4.94970e23	−	8.57313e23i	−0.848808	−	1.47018i
$239$	−7.94811e23	+	4.58885e23i	−1.30703	+	0.754613i	−0.981599	−	0.190953i	$-0.938842\pi$
$239$	−7.94811e23	+	4.58885e23i	−1.30703	+	0.754613i	−0.325430	+	0.945566i	$0.605509\pi$
$240$		0			0
$241$	1.97126e23	−	3.41432e23i	0.298245	−	0.516575i	−0.677490	−	0.735532i	$-0.736932\pi$
$241$	1.97126e23	−	3.41432e23i	0.298245	−	0.516575i	0.975734	+	0.218957i	$0.0702655\pi$
$242$			4.51754e23i			0.655766i
$243$		0			0
$244$	−2.30966e23			−0.308780
$245$	−2.37701e23	−	1.37237e23i	−0.305050	−	0.176121i
$246$		0			0
$247$	3.69075e22	+	6.39257e22i	0.0436662	+	0.0756321i
$248$	9.55742e22	−	5.51798e22i	0.108599	−	0.0626994i
$249$		0			0
$250$	−3.56654e23	+	6.17742e23i	−0.373979	+	0.647750i
$251$			2.86762e23i			0.288924i	0.989510	+	0.144462i	$0.0461452\pi$
$251$			2.86762e23i			0.288924i	−0.989510	+	0.144462i	$0.953855\pi$
$252$		0			0
$253$	1.59736e24			1.48662
$254$	8.91736e23	+	5.14844e23i	0.797809	+	0.460615i
$255$		0			0
$256$	−3.77789e22	−	6.54350e22i	−0.0312500	−	0.0541266i
$257$	−1.35266e24	+	7.80958e23i	−1.07611	+	0.621293i	−0.929845	−	0.367952i	$-0.880059\pi$
$257$	−1.35266e24	+	7.80958e23i	−1.07611	+	0.621293i	−0.146266	+	0.989245i	$0.546726\pi$
$258$		0			0
$259$	−6.39644e23	+	1.10790e24i	−0.470913	+	0.815645i
$260$		−	3.91927e23i		−	0.277633i
$261$		0			0
$262$	−8.47976e23			−0.556379
$263$	1.87714e24	+	1.08377e24i	1.18560	+	0.684508i	0.957304	−	0.289083i	$-0.0933502\pi$
$263$	1.87714e24	+	1.08377e24i	1.18560	+	0.684508i	0.228299	+	0.973591i	$0.426684\pi$
$264$		0			0
$265$	−4.62897e23	−	8.01762e23i	−0.271035	−	0.469447i
$266$	−1.46848e23	+	8.47827e22i	−0.0828040	+	0.0478069i
$267$		0			0
$268$	8.70213e23	−	1.50725e24i	0.455279	−	0.788566i
$269$		−	2.41699e24i		−	1.21830i	−0.793057	−	0.609148i	$-0.791512\pi$
$269$		−	2.41699e24i		−	1.21830i	0.793057	−	0.609148i	$-0.208488\pi$
$270$		0			0
$271$	−3.73186e24			−1.74676			−0.873378	−	0.487042i	$-0.838076\pi$
$271$	−3.73186e24			−1.74676			−0.873378	+	0.487042i	$0.838076\pi$
$272$	9.40063e23	+	5.42746e23i	0.424100	+	0.244854i
$273$		0			0
$274$	−1.33704e23	−	2.31582e23i	−0.0560580	−	0.0970953i
$275$	−1.51065e24	+	8.72172e23i	−0.610711	+	0.352594i
$276$		0			0
$277$	−2.02418e24	+	3.50598e24i	−0.761117	+	1.31829i	0.181157	+	0.983454i	$0.442016\pi$
$277$	−2.02418e24	+	3.50598e24i	−0.761117	+	1.31829i	−0.942275	+	0.334840i	$0.891318\pi$
$278$			3.38836e23i			0.122897i
$279$		0			0
$280$	9.00321e23			0.303960
$281$	2.04185e24	+	1.17886e24i	0.665212	+	0.384061i	0.794260	−	0.607578i	$-0.207859\pi$
$281$	2.04185e24	+	1.17886e24i	0.665212	+	0.384061i	−0.129048	+	0.991638i	$0.541192\pi$
$282$		0			0
$283$	7.01417e23	+	1.21489e24i	0.212869	+	0.368700i	0.952611	−	0.304191i	$-0.0983859\pi$
$283$	7.01417e23	+	1.21489e24i	0.212869	+	0.368700i	−0.739742	+	0.672890i	$0.765053\pi$
$284$	−1.45705e24	+	8.41229e23i	−0.426866	+	0.246451i
$285$		0			0
$286$	1.42265e24	−	2.46410e24i	0.388541	−	0.672973i
$287$			3.98996e24i			1.05232i
$288$		0			0
$289$	−1.15303e25			−2.83703
$290$	2.09882e24	+	1.21176e24i	0.498880	+	0.288028i
$291$		0			0
$292$	1.83614e24	+	3.18029e24i	0.407453	+	0.705730i
$293$	3.04569e23	−	1.75843e23i	0.0653144	−	0.0377093i	−0.466987	−	0.884264i	$-0.654661\pi$
$293$	3.04569e23	−	1.75843e23i	0.0653144	−	0.0377093i	0.532302	+	0.846555i	$0.321327\pi$
$294$		0			0
$295$	−2.56524e24	+	4.44313e24i	−0.513935	+	0.890161i
$296$		−	1.40277e24i		−	0.271687i
$297$		0			0
$298$	2.11012e24			0.382072
$299$	−4.19230e24	−	2.42043e24i	−0.734076	−	0.423819i
$300$		0			0
$301$	−3.76464e24	−	6.52054e24i	−0.616677	−	1.06812i
$302$	3.46196e24	−	1.99877e24i	0.548596	−	0.316732i
$303$		0			0
$304$	9.29661e22	−	1.61022e23i	0.0137908	−	0.0238863i
$305$			3.01775e24i			0.433196i
$306$		0			0
$307$	9.66992e24			1.30029			0.650143	−	0.759811i	$-0.274709\pi$
$307$	9.66992e24			1.30029			0.650143	+	0.759811i	$0.274709\pi$
$308$	5.66044e24	+	3.26805e24i	0.736788	+	0.425385i
$309$		0			0
$310$	−7.20967e23	−	1.24875e24i	−0.0879627	−	0.152356i
$311$	1.42746e24	−	8.24145e23i	0.168640	−	0.0973643i	−0.413304	−	0.910593i	$-0.635625\pi$
$311$	1.42746e24	−	8.24145e23i	0.168640	−	0.0973643i	0.581944	+	0.813229i	$0.302292\pi$
$312$		0			0
$313$	2.61512e24	−	4.52952e24i	0.289766	−	0.501890i	−0.683988	−	0.729494i	$-0.739756\pi$
$313$	2.61512e24	−	4.52952e24i	0.289766	−	0.501890i	0.973754	+	0.227604i	$0.0730891\pi$
$314$		−	4.23214e24i		−	0.454217i
$315$		0			0
$316$	−2.79029e24			−0.281046
$317$	−3.02405e24	−	1.74594e24i	−0.295118	−	0.170387i	0.345129	−	0.938555i	$-0.387835\pi$
$317$	−3.02405e24	−	1.74594e24i	−0.295118	−	0.170387i	−0.640248	+	0.768168i	$0.721168\pi$
$318$		0			0
$319$	8.79705e24	+	1.52369e25i	0.806177	+	1.39634i
$320$	−8.54959e23	+	4.93611e23i	−0.0759356	+	0.0438415i
$321$		0			0
$322$	5.56012e24	−	9.63041e24i	0.464008	−	0.803685i
$323$			2.67117e24i			0.216111i
$324$		0			0
$325$	5.28628e24			0.402084
$326$	−3.07575e24	−	1.77579e24i	−0.226869	−	0.130983i
$327$		0			0
$328$	−2.18754e24	−	3.78893e24i	−0.151781	−	0.262892i
$329$	−2.05171e25	+	1.18456e25i	−1.38088	+	0.797254i
$330$		0			0
$331$	−1.12996e25	+	1.95715e25i	−0.715788	+	1.23978i	0.246866	+	0.969050i	$0.420599\pi$
$331$	−1.12996e25	+	1.95715e25i	−0.715788	+	1.23978i	−0.962655	+	0.270732i	$0.912734\pi$
$332$		−	2.31777e24i		−	0.142459i
$333$		0			0
$334$	2.01887e25			1.16854
$335$	−1.96934e25	−	1.13700e25i	−1.10630	−	0.638723i
$336$		0			0
$337$	1.13293e24	+	1.96228e24i	0.0599656	+	0.103863i	0.894450	−	0.447168i	$-0.147568\pi$
$337$	1.13293e24	+	1.96228e24i	0.0599656	+	0.103863i	−0.834484	+	0.551032i	$0.814234\pi$
$338$	4.44992e24	−	2.56916e24i	0.228657	−	0.132015i
$339$		0			0
$340$	7.09140e24	−	1.22827e25i	0.343512	−	0.594981i
$341$		−	1.04681e25i		−	0.492406i
$342$		0			0
$343$	1.37529e25			0.610174
$344$	7.14992e24	+	4.12801e24i	0.308118	+	0.177892i
$345$		0			0
$346$	6.36884e23	+	1.10311e24i	0.0259000	+	0.0448601i
$347$	−3.41332e24	+	1.97068e24i	−0.134860	+	0.0778612i	−0.565912	−	0.824466i	$-0.691476\pi$
$347$	−3.41332e24	+	1.97068e24i	−0.134860	+	0.0778612i	0.431052	+	0.902327i	$0.358142\pi$
$348$		0			0
$349$	2.00427e25	−	3.47149e25i	0.747655	−	1.29498i	−0.201289	−	0.979532i	$-0.564513\pi$
$349$	2.00427e25	−	3.47149e25i	0.747655	−	1.29498i	0.948944	−	0.315445i	$-0.102154\pi$
$350$			1.21435e25i			0.440212i
$351$		0			0
$352$	−7.16699e24			−0.245420
$353$	−1.51856e25	−	8.76738e24i	−0.505456	−	0.291825i	0.225508	−	0.974241i	$-0.427596\pi$
$353$	−1.51856e25	−	8.76738e24i	−0.505456	−	0.291825i	−0.730964	+	0.682416i	$0.760929\pi$
$354$		0			0
$355$	1.09913e25	+	1.90375e25i	0.345753	+	0.598862i
$356$	2.28046e25	−	1.31662e25i	0.697464	−	0.402681i
$357$		0			0
$358$	1.78349e25	−	3.08909e25i	0.515751	−	0.893306i
$359$		−	5.46046e25i		−	1.53562i	−0.640675	−	0.767812i	$-0.721345\pi$
$359$		−	5.46046e25i		−	1.53562i	0.640675	−	0.767812i	$-0.278655\pi$
$360$		0			0
$361$	−3.71324e25			−0.987828
$362$	3.31434e25	+	1.91353e25i	0.857651	+	0.495165i
$363$		0			0
$364$	−9.90393e24	−	1.71541e25i	−0.242546	−	0.420101i
$365$	4.15530e25	−	2.39906e25i	0.990087	−	0.571627i
$366$		0			0
$367$	−4.86765e24	+	8.43101e24i	−0.109814	+	0.190204i	−0.915695	−	0.401874i	$-0.868359\pi$
$367$	−4.86765e24	+	8.43101e24i	−0.109814	+	0.190204i	0.805881	+	0.592078i	$0.201692\pi$
$368$			1.21936e25i			0.267703i
$369$		0			0
$370$	−1.83283e25			−0.381157
$371$	−4.05208e25	−	2.33947e25i	−0.820235	−	0.473563i
$372$		0			0
$373$	4.62911e25	+	8.01786e25i	0.887993	+	1.53805i	0.842244	+	0.539096i	$0.181234\pi$
$373$	4.62911e25	+	8.01786e25i	0.887993	+	1.53805i	0.0457489	+	0.998953i	$0.485433\pi$
$374$	8.91691e25	−	5.14818e25i	1.66532	−	0.961474i
$375$		0			0
$376$	1.29889e25	−	2.24975e25i	0.229983	−	0.398341i
$377$		−	5.33194e25i		−	0.919331i
$378$		0			0
$379$	6.30876e24			0.103170			0.0515849	−	0.998669i	$-0.483573\pi$
$379$	6.30876e24			0.103170			0.0515849	+	0.998669i	$0.483573\pi$
$380$	−2.10388e24	−	1.21467e24i	−0.0335108	−	0.0193475i
$381$		0			0
$382$	−8.34071e24	−	1.44465e25i	−0.126058	−	0.218338i
$383$	1.89045e25	−	1.09145e25i	0.278341	−	0.160700i	−0.354331	−	0.935120i	$-0.615291\pi$
$383$	1.89045e25	−	1.09145e25i	0.278341	−	0.160700i	0.632672	+	0.774420i	$0.281958\pi$
$384$		0			0
$385$	4.26997e25	−	7.39580e25i	0.596784	−	1.03366i
$386$		−	3.05324e25i		−	0.415803i
$387$		0			0
$388$	5.55860e24			0.0718866
$389$	−7.42188e24	−	4.28503e24i	−0.0935444	−	0.0540079i	0.452498	−	0.891765i	$-0.350533\pi$
$389$	−7.42188e24	−	4.28503e24i	−0.0935444	−	0.0540079i	−0.546042	+	0.837757i	$0.683866\pi$
$390$		0			0
$391$	−8.75888e25	−	1.51708e26i	−1.04877	−	1.81653i
$392$	1.31729e25	−	7.60538e24i	0.153752	−	0.0887687i
$393$		0			0
$394$	1.32898e25	−	2.30186e25i	0.147420	−	0.255339i
$395$			3.64572e25i			0.394287i
$396$		0			0
$397$	−1.05722e26			−1.08708			−0.543538	−	0.839384i	$-0.682916\pi$
$397$	−1.05722e26			−1.08708			−0.543538	+	0.839384i	$0.682916\pi$
$398$	−7.65827e24	−	4.42151e24i	−0.0767892	−	0.0443343i
$399$		0			0
$400$	−6.65779e24	−	1.15316e25i	−0.0634936	−	0.109974i
$401$	−1.78718e26	+	1.03183e26i	−1.66236	+	0.959762i	−0.690771	+	0.723074i	$0.742729\pi$
$401$	−1.78718e26	+	1.03183e26i	−1.66236	+	0.959762i	−0.971586	+	0.236688i	$0.923938\pi$
$402$		0			0
$403$	−1.58619e25	+	2.74736e25i	−0.140380	+	0.243145i
$404$		−	8.26317e24i		−	0.0713400i
$405$		0			0
$406$	1.22483e26			1.00651
$407$	−1.15232e26	−	6.65293e25i	−0.923910	−	0.533420i
$408$		0			0
$409$	1.19841e26	+	2.07571e26i	0.914897	+	1.58465i	0.807053	+	0.590479i	$0.201061\pi$
$409$	1.19841e26	+	2.07571e26i	0.914897	+	1.58465i	0.107844	+	0.994168i	$0.465605\pi$
$410$	−4.95053e25	+	2.85819e25i	−0.368819	+	0.212938i
$411$		0			0
$412$	−6.85064e24	+	1.18656e25i	−0.0486137	+	0.0842014i
$413$			2.59293e26i			1.79593i
$414$		0			0
$415$	−3.02834e25			−0.199859
$416$	1.88099e25	+	1.08599e25i	0.121186	+	0.0699667i
$417$		0			0
$418$	−8.81824e24	−	1.52736e25i	−0.0541526	−	0.0937950i
$419$	1.07118e26	−	6.18445e25i	0.642276	−	0.370818i	−0.143215	−	0.989692i	$-0.545744\pi$
$419$	1.07118e26	−	6.18445e25i	0.642276	−	0.370818i	0.785491	+	0.618873i	$0.212411\pi$
$420$		0			0
$421$	−1.09562e26	+	1.89767e26i	−0.626383	+	1.08493i	0.361889	+	0.932221i	$0.382132\pi$
$421$	−1.09562e26	+	1.89767e26i	−0.626383	+	1.08493i	−0.988272	+	0.152706i	$0.951201\pi$
$422$			8.18861e25i			0.457178i
$423$		0			0
$424$	5.13056e25			0.273216
$425$	1.65668e26	+	9.56482e25i	0.861684	+	0.497494i
$426$		0			0
$427$	7.62579e25	+	1.32083e26i	0.378448	+	0.655491i
$428$	−1.89107e24	+	1.09181e24i	−0.00916791	+	0.00529310i
$429$		0			0
$430$	5.39356e25	−	9.34192e25i	0.249569	−	0.432267i
$431$		−	1.34215e26i		−	0.606776i	−0.952867	−	0.303388i	$-0.901882\pi$
$431$		−	1.34215e26i		−	0.606776i	0.952867	−	0.303388i	$-0.0981178\pi$
$432$		0			0
$433$	−7.52121e25			−0.324645			−0.162323	−	0.986738i	$-0.551899\pi$
$433$	−7.52121e25			−0.324645			−0.162323	+	0.986738i	$0.551899\pi$
$434$	−6.31115e25	−	3.64374e25i	−0.266202	−	0.153692i
$435$		0			0
$436$	1.07148e26	+	1.85585e26i	0.431636	+	0.747616i
$437$	−2.59859e25	+	1.50029e25i	−0.102311	+	0.0590694i
$438$		0			0
$439$	−7.41514e25	+	1.28434e26i	−0.278916	+	0.483097i	−0.971116	−	0.238609i	$-0.923309\pi$
$439$	−7.41514e25	+	1.28434e26i	−0.278916	+	0.483097i	0.692199	+	0.721706i	$0.256642\pi$
$440$			9.36423e25i			0.344306i
$441$		0			0
$442$	−3.12034e26			−1.09643
$443$	−2.89401e25	−	1.67086e25i	−0.0994176	−	0.0573988i	0.449467	−	0.893297i	$-0.351614\pi$
$443$	−2.89401e25	−	1.67086e25i	−0.0994176	−	0.0573988i	−0.548884	+	0.835898i	$0.684947\pi$
$444$		0			0
$445$	−1.72027e26	−	2.97959e26i	−0.564932	−	0.978492i
$446$	−1.18256e26	+	6.82751e25i	−0.379730	+	0.219237i
$447$		0			0
$448$	−2.49469e25	+	4.32093e25i	−0.0766014	+	0.132678i
$449$			6.34676e26i			1.90585i	0.303207	+	0.952925i	$0.401943\pi$
$449$			6.34676e26i			1.90585i	−0.303207	+	0.952925i	$0.598057\pi$
$450$		0			0
$451$	−4.14995e26			−1.19200
$452$	1.72186e26	+	9.94116e25i	0.483742	+	0.279288i
$453$		0			0
$454$	7.01468e25	+	1.21498e26i	0.188560	+	0.326595i
$455$	−2.24132e26	+	1.29402e26i	−0.589372	+	0.340274i
$456$		0			0
$457$	2.24391e26	−	3.88656e26i	0.564732	−	0.978145i	−0.432342	−	0.901710i	$-0.642313\pi$
$457$	2.24391e26	−	3.88656e26i	0.564732	−	0.978145i	0.997075	−	0.0764357i	$-0.0243540\pi$
$458$			3.44331e26i			0.847854i
$459$		0			0
$460$	1.59319e26			0.375568
$461$	1.22822e26	+	7.09115e25i	0.283314	+	0.163571i	0.634923	−	0.772576i	$-0.281032\pi$
$461$	1.22822e26	+	7.09115e25i	0.283314	+	0.163571i	−0.351609	+	0.936147i	$0.614365\pi$
$462$		0			0
$463$	3.74798e26	+	6.49169e26i	0.827917	+	1.43399i	0.899669	+	0.436572i	$0.143808\pi$
$463$	3.74798e26	+	6.49169e26i	0.827917	+	1.43399i	−0.0717518	+	0.997423i	$0.522859\pi$
$464$	−1.16312e26	+	6.71529e25i	−0.251447	+	0.145173i
$465$		0			0
$466$	−4.76649e25	+	8.25581e25i	−0.0987052	+	0.170962i
$467$			3.69852e26i			0.749650i	0.927096	+	0.374825i	$0.122297\pi$
$467$			3.69852e26i			0.749650i	−0.927096	+	0.374825i	$0.877703\pi$
$468$		0			0
$469$	−1.14927e27			−2.23200
$470$	−2.93947e26	−	1.69710e26i	−0.558844	−	0.322649i
$471$		0			0
$472$	−1.42160e26	−	2.46229e26i	−0.259035	−	0.448661i
$473$	6.78201e26	−	3.91559e26i	1.20989	−	0.698532i
$474$		0			0
$475$	1.63834e25	−	2.83769e25i	0.0280201	−	0.0485322i
$476$		−	7.16793e26i		−	1.20040i
$477$		0			0
$478$	−6.64536e26			−1.06718
$479$	−4.41847e26	−	2.55101e26i	−0.694892	−	0.401196i	0.110550	−	0.993871i	$-0.464739\pi$
$479$	−4.41847e26	−	2.55101e26i	−0.694892	−	0.401196i	−0.805442	+	0.592675i	$0.798072\pi$
$480$		0			0
$481$	2.01619e26	+	3.49214e26i	0.304145	+	0.526794i
$482$	2.47223e26	−	1.42734e26i	0.365274	−	0.210891i
$483$		0			0
$484$	−1.63553e26	+	2.83281e26i	−0.231848	+	0.401573i
$485$		−	7.26274e25i		−	0.100852i
$486$		0			0
$487$	−4.25959e26			−0.567646			−0.283823	−	0.958877i	$-0.591603\pi$
$487$	−4.25959e26			−0.567646			−0.283823	+	0.958877i	$0.591603\pi$
$488$	−1.44832e26	−	8.36185e25i	−0.189088	−	0.109170i
$489$		0			0
$490$	−9.93701e25	−	1.72114e26i	−0.124536	−	0.215703i
$491$	7.58761e26	−	4.38071e26i	0.931730	−	0.537935i	0.0443719	−	0.999015i	$-0.485871\pi$
$491$	7.58761e26	−	4.38071e26i	0.931730	−	0.537935i	0.887358	+	0.461080i	$0.152538\pi$
$492$		0			0
$493$	9.64743e26	−	1.67098e27i	1.13748	−	1.97017i
$494$			5.34478e25i			0.0617533i
$495$		0			0
$496$	7.99089e25			0.0886703
$497$	9.62149e26	+	5.55497e26i	1.04635	+	0.604112i
$498$		0			0
$499$	9.33699e26	+	1.61721e27i	0.975442	+	1.68952i	0.678468	+	0.734630i	$0.262644\pi$
$499$	9.33699e26	+	1.61721e27i	0.975442	+	1.68952i	0.296974	+	0.954886i	$0.404023\pi$
$500$	−4.47293e26	+	2.58245e26i	−0.458028	+	0.264443i
$501$		0			0
$502$	−1.03819e26	+	1.79820e26i	−0.102150	+	0.176929i
$503$		−	1.15358e27i		−	1.11267i	−0.830956	−	0.556337i	$-0.812206\pi$
$503$		−	1.15358e27i		−	1.11267i	0.830956	−	0.556337i	$-0.187794\pi$
$504$		0			0
$505$	−1.07965e26			−0.100085
$506$	1.00166e27	+	5.78307e26i	0.910362	+	0.525598i
$507$		0			0
$508$	3.72787e26	+	6.45686e26i	0.325704	+	0.564136i
$509$	−1.82376e27	+	1.05295e27i	−1.56239	+	0.902049i	−0.565380	+	0.824831i	$0.691270\pi$
$509$	−1.82376e27	+	1.05295e27i	−1.56239	+	0.902049i	−0.997014	+	0.0772180i	$0.975396\pi$
$510$		0			0
$511$	1.21248e27	−	2.10007e27i	0.998768	−	1.72992i
$512$		−	5.47097e25i		−	0.0441942i
$513$		0			0
$514$	−1.13095e27			−0.878641
$515$	1.55034e26	+	8.95089e25i	0.118128	+	0.0682015i
$516$		0			0
$517$	−1.23206e27	−	2.13398e27i	−0.903077	−	1.56418i
$518$	−8.02202e26	+	4.63152e26i	−0.576748	+	0.332986i
$519$		0			0
$520$	1.41893e26	−	2.45765e26i	0.0981582	−	0.170015i
$521$		−	2.24374e27i		−	1.52264i	−0.648379	−	0.761318i	$-0.724553\pi$
$521$		−	2.24374e27i		−	1.52264i	0.648379	−	0.761318i	$-0.275447\pi$
$522$		0			0
$523$	2.32737e27			1.52002			0.760008	−	0.649914i	$-0.225195\pi$
$523$	2.32737e27			1.52002			0.760008	+	0.649914i	$0.225195\pi$
$524$	−5.31740e26	−	3.07000e26i	−0.340711	−	0.196710i
$525$		0			0
$526$	7.84732e26	+	1.35920e27i	0.484021	+	0.838348i
$527$	−9.94197e26	+	5.74000e26i	−0.601681	+	0.347381i
$528$		0			0
$529$	1.25828e26	−	2.17941e26i	0.0733197	−	0.126994i
$530$		−	6.70347e26i		−	0.383302i
$531$		0			0
$532$	−1.22778e26			−0.0676092
$533$	1.08916e27	+	6.28827e26i	0.588599	+	0.339828i
$534$		0			0
$535$	1.42654e25	+	2.47083e25i	0.00742583	+	0.0128619i
$536$	1.09137e27	−	6.30101e26i	0.557600	−	0.321931i
$537$		0			0
$538$	8.75045e26	−	1.51562e27i	0.430732	−	0.746050i
$539$		−	1.44281e27i		−	0.697140i
$540$		0			0
$541$	2.86087e27			1.33206			0.666032	−	0.745923i	$-0.267991\pi$
$541$	2.86087e27			1.33206			0.666032	+	0.745923i	$0.267991\pi$
$542$	−2.34014e27	−	1.35108e27i	−1.06967	−	0.617572i
$543$		0			0
$544$	3.92990e26	+	6.80679e26i	0.173138	+	0.299884i
$545$	2.42481e27	−	1.39997e27i	1.04885	−	0.605554i
$546$		0			0
$547$	−1.05474e26	+	1.82686e26i	−0.0439816	+	0.0761784i	−0.887178	−	0.461427i	$-0.847338\pi$
$547$	−1.05474e26	+	1.82686e26i	−0.0439816	+	0.0761784i	0.843197	+	0.537605i	$0.180671\pi$
$548$		−	1.93624e26i		−	0.0792780i
$549$		0			0
$550$	−1.26304e27			−0.498644
$551$	−2.86220e26	−	1.65249e26i	−0.110965	−	0.0640654i
$552$		0			0
$553$	9.21268e26	+	1.59568e27i	0.344457	+	0.596617i
$554$	−2.53860e27	+	1.46566e27i	−0.932175	+	0.538191i
$555$		0			0
$556$	−1.22672e26	+	2.12474e26i	−0.0434507	+	0.0752589i
$557$		−	7.58693e26i		−	0.263945i	−0.991253	−	0.131973i	$-0.957869\pi$
$557$		−	7.58693e26i		−	0.263945i	0.991253	−	0.131973i	$-0.0421311\pi$
$558$		0			0
$559$	−2.37326e27			−0.796577
$560$	5.64564e26	+	3.25951e26i	0.186137	+	0.107466i
$561$		0			0
$562$	8.53587e26	+	1.47846e27i	0.271572	+	0.470376i
$563$	2.99845e27	−	1.73115e27i	0.937157	−	0.541068i	0.0480891	−	0.998843i	$-0.484687\pi$
$563$	2.99845e27	−	1.73115e27i	0.937157	−	0.541068i	0.889068	+	0.457775i	$0.151354\pi$
$564$		0			0
$565$	1.29889e27	−	2.24974e27i	0.391821	−	0.678654i
$566$			1.01576e27i			0.301042i
$567$		0			0
$568$	−1.21823e27			−0.348535
$569$	9.04409e26	+	5.22161e26i	0.254239	+	0.146785i	0.621704	−	0.783253i	$-0.286441\pi$
$569$	9.04409e26	+	5.22161e26i	0.254239	+	0.146785i	−0.367465	+	0.930037i	$0.619774\pi$
$570$		0			0
$571$	8.12384e26	+	1.40709e27i	0.220496	+	0.381910i	0.954959	−	0.296739i	$-0.0958992\pi$
$571$	8.12384e26	+	1.40709e27i	0.220496	+	0.381910i	−0.734463	+	0.678649i	$0.762566\pi$
$572$	1.78420e27	−	1.03011e27i	0.475864	−	0.274740i
$573$		0			0
$574$	−1.44452e27	+	2.50198e27i	−0.372053	+	0.644414i
$575$			2.14888e27i			0.543918i
$576$		0			0
$577$	3.69616e26			0.0903634			0.0451817	−	0.998979i	$-0.485613\pi$
$577$	3.69616e26			0.0903634			0.0451817	+	0.998979i	$0.485613\pi$
$578$	−7.23032e27	−	4.17443e27i	−1.73732	−	1.00304i
$579$		0			0
$580$	8.77405e26	+	1.51971e27i	0.203667	+	0.352761i
$581$	−1.32546e27	+	7.65257e26i	−0.302417	+	0.174601i
$582$		0			0
$583$	2.43328e27	−	4.21456e27i	0.536421	−	0.929109i
$584$			2.65902e27i			0.576226i
$585$		0			0
$586$	2.54648e26			0.0533290
$587$	7.47291e27	+	4.31449e27i	1.53854	+	0.888277i	0.998925	+	0.0463658i	$0.0147640\pi$
$587$	7.47291e27	+	4.31449e27i	1.53854	+	0.888277i	0.539616	+	0.841911i	$0.318569\pi$
$588$		0			0
$589$	9.83196e25	+	1.70295e26i	0.0195653	+	0.0338881i
$590$	−3.21717e27	+	1.85743e27i	−0.629439	+	0.363407i
$591$		0			0
$592$	5.07856e26	−	8.79633e26i	0.0960558	−	0.166374i
$593$		−	7.23061e27i		−	1.34471i	−0.740230	−	0.672354i	$-0.765283\pi$
$593$		−	7.23061e27i		−	1.34471i	0.740230	−	0.672354i	$-0.234717\pi$
$594$		0			0
$595$	−9.36546e27			−1.68407
$596$	1.32319e27	+	7.63947e26i	0.233971	+	0.135083i
$597$		0			0
$598$	−1.75258e27	−	3.03555e27i	−0.299685	−	0.519070i
$599$	3.79481e27	−	2.19093e27i	0.638148	−	0.368435i	−0.145753	−	0.989321i	$-0.546560\pi$
$599$	3.79481e27	−	2.19093e27i	0.638148	−	0.368435i	0.783901	+	0.620886i	$0.213227\pi$
$600$		0			0
$601$	3.41261e27	−	5.91082e27i	0.555063	−	0.961398i	−0.442835	−	0.896603i	$-0.646027\pi$
$601$	3.41261e27	−	5.91082e27i	0.555063	−	0.961398i	0.997899	−	0.0647949i	$-0.0206393\pi$
$602$		−	5.45177e27i		−	0.872113i
$603$		0			0
$604$	2.89452e27			0.447927
$605$	3.70129e27	+	2.13694e27i	0.563377	+	0.325266i
$606$		0			0
$607$	3.72113e27	+	6.44518e27i	0.548009	+	0.949179i	0.998411	+	0.0563533i	$0.0179473\pi$
$607$	3.72113e27	+	6.44518e27i	0.548009	+	0.949179i	−0.450402	+	0.892826i	$0.648719\pi$
$608$	1.16592e26	−	6.73147e25i	0.0168902	−	0.00975155i
$609$		0			0
$610$	−1.09254e27	+	1.89234e27i	−0.153158	+	0.265277i
$611$			7.46756e27i			1.02983i
$612$		0			0
$613$	−2.51368e27			−0.335510			−0.167755	−	0.985829i	$-0.553652\pi$
$613$	−2.51368e27			−0.335510			−0.167755	+	0.985829i	$0.553652\pi$
$614$	6.06371e27	+	3.50089e27i	0.796260	+	0.459721i
$615$		0			0
$616$	2.36632e27	+	4.09859e27i	0.300793	+	0.520988i
$617$	−1.29761e28	+	7.49174e27i	−1.62290	+	0.936982i	−0.636761	+	0.771061i	$0.719726\pi$
$617$	−1.29761e28	+	7.49174e27i	−1.62290	+	0.936982i	−0.986139	+	0.165921i	$0.946940\pi$
$618$		0			0
$619$	6.45322e26	−	1.11773e27i	0.0781394	−	0.135341i	−0.824308	−	0.566142i	$-0.808435\pi$
$619$	6.45322e26	−	1.11773e27i	0.0781394	−	0.135341i	0.902447	+	0.430801i	$0.141769\pi$
$620$		−	1.04407e27i		−	0.124398i
$621$		0			0
$622$	1.19349e27			0.137694
$623$	−1.50588e28	−	8.69418e27i	−1.70966	−	0.987071i
$624$		0			0
$625$	1.06429e27	+	1.84340e27i	0.117019	+	0.202684i
$626$	3.27972e27	−	1.89355e27i	0.354890	−	0.204896i
$627$		0			0
$628$	1.53220e27	−	2.65385e27i	0.160590	−	0.278150i
$629$			1.45921e28i			1.50526i
$630$		0			0
$631$	−3.97000e27			−0.396732			−0.198366	−	0.980128i	$-0.563563\pi$
$631$	−3.97000e27			−0.396732			−0.198366	+	0.980128i	$0.563563\pi$
$632$	−1.74970e27	−	1.01019e27i	−0.172105	−	0.0993648i
$633$		0			0
$634$	−1.26419e27	−	2.18965e27i	−0.120482	−	0.208680i
$635$	8.43638e27	−	4.87075e27i	0.791442	−	0.456939i
$636$		0			0
$637$	−2.18623e27	+	3.78666e27i	−0.198748	+	0.344241i
$638$			1.27395e28i			1.14011i
$639$		0			0
$640$	−7.14825e26			−0.0620012
$641$	−9.82663e27	−	5.67341e27i	−0.839121	−	0.484467i	0.0178446	−	0.999841i	$-0.494320\pi$
$641$	−9.82663e27	−	5.67341e27i	−0.839121	−	0.484467i	−0.856965	+	0.515374i	$0.827653\pi$
$642$		0			0
$643$	−7.40078e27	−	1.28185e28i	−0.612587	−	1.06103i	−0.990803	−	0.135314i	$-0.956796\pi$
$643$	−7.40078e27	−	1.28185e28i	−0.612587	−	1.06103i	0.378216	−	0.925717i	$-0.376538\pi$
$644$	6.97316e27	−	4.02596e27i	0.568291	−	0.328103i
$645$		0			0
$646$	−9.67067e26	+	1.67501e27i	−0.0764067	+	0.132340i
$647$		−	1.75706e27i		−	0.136692i	−0.997662	−	0.0683460i	$-0.978228\pi$
$647$		−	1.75706e27i		−	0.136692i	0.997662	−	0.0683460i	$-0.0217722\pi$
$648$		0			0
$649$	−2.69690e28			−2.03431
$650$	3.31487e27	+	1.91384e27i	0.246225	+	0.142158i
$651$		0			0
$652$	−1.28581e27	−	2.22708e27i	−0.0926189	−	0.160421i
$653$	6.46890e27	−	3.73482e27i	0.458880	−	0.264934i	−0.252693	−	0.967546i	$-0.581316\pi$
$653$	6.46890e27	−	3.73482e27i	0.458880	−	0.264934i	0.711573	+	0.702612i	$0.247983\pi$
$654$		0			0
$655$	−4.01119e27	+	6.94759e27i	−0.275969	+	0.477993i
$656$		−	3.16789e27i		−	0.214651i
$657$		0			0
$658$	−1.71542e28			−1.12749
$659$	1.23415e27	+	7.12537e26i	0.0798940	+	0.0461268i	0.539415	−	0.842040i	$-0.318646\pi$
$659$	1.23415e27	+	7.12537e26i	0.0798940	+	0.0461268i	−0.459521	+	0.888167i	$0.651979\pi$
$660$		0			0
$661$	8.52779e27	+	1.47706e28i	0.535577	+	0.927647i	0.999135	+	0.0415803i	$0.0132392\pi$
$661$	8.52779e27	+	1.47706e28i	0.535577	+	0.927647i	−0.463558	+	0.886067i	$0.653427\pi$
$662$	−1.41713e28	+	8.18181e27i	−0.876658	+	0.506139i
$663$		0			0
$664$	8.39122e26	−	1.45340e27i	0.0503668	−	0.0872378i
$665$			1.60420e27i			0.0948508i
$666$		0			0
$667$	2.16744e28			1.24362
$668$	1.26597e28	+	7.30911e27i	0.715583	+	0.413142i
$669$		0			0
$670$	−8.23276e27	−	1.42596e28i	−0.451645	−	0.782273i
$671$	−1.37379e28	+	7.93158e27i	−0.742497	+	0.428681i
$672$		0			0
$673$	−1.55981e28	+	2.70167e28i	−0.818316	+	1.41737i	0.0886059	+	0.996067i	$0.471759\pi$
$673$	−1.55981e28	+	2.70167e28i	−0.818316	+	1.41737i	−0.906922	+	0.421298i	$0.861575\pi$
$674$			1.64065e27i			0.0848042i
$675$		0			0
$676$	3.72054e27			0.186698
$677$	1.52047e28	+	8.77843e27i	0.751780	+	0.434040i	0.826337	−	0.563177i	$-0.190421\pi$
$677$	1.52047e28	+	8.77843e27i	0.751780	+	0.434040i	−0.0745569	+	0.997217i	$0.523754\pi$
$678$		0			0
$679$	−1.83528e27	−	3.17880e27i	−0.0881059	−	0.152604i
$680$	8.89359e27	−	5.13472e27i	0.420715	−	0.242900i
$681$		0			0
$682$	3.78985e27	−	6.56422e27i	0.174092	−	0.301536i
$683$			2.50615e28i			1.13449i	0.823550	+	0.567244i	$0.191990\pi$
$683$			2.50615e28i			1.13449i	−0.823550	+	0.567244i	$0.808010\pi$
$684$		0			0
$685$	−2.52984e27			−0.111221
$686$	8.62404e27	+	4.97909e27i	0.373654	+	0.215729i
$687$		0			0
$688$	2.98900e27	+	5.17709e27i	0.125789	+	0.217872i
$689$	−1.27723e28	+	7.37411e27i	−0.529759	+	0.305856i
$690$		0			0
$691$	1.22623e27	−	2.12389e27i	0.0494072	−	0.0855758i	−0.840264	−	0.542177i	$-0.817600\pi$
$691$	1.22623e27	−	2.12389e27i	0.0494072	−	0.0855758i	0.889671	+	0.456601i	$0.150933\pi$
$692$			9.22306e26i			0.0366281i
$693$		0			0
$694$	−2.85385e27			−0.110112
$695$	2.77614e27	+	1.60280e27i	0.105583	+	0.0609582i
$696$		0			0
$697$	2.27556e28	+	3.94138e28i	0.840930	+	1.45653i
$698$	2.51363e28	−	1.45124e28i	0.915687	−	0.528672i
$699$		0			0
$700$	−4.39640e27	+	7.61479e27i	−0.155639	+	0.269574i
$701$		−	3.01435e28i		−	1.05199i	−0.850486	−	0.525997i	$-0.823692\pi$
$701$		−	3.01435e28i		−	1.05199i	0.850486	−	0.525997i	$-0.176308\pi$
$702$		0			0
$703$	2.49946e27			0.0847798
$704$	−4.49420e27	−	2.59473e27i	−0.150289	−	0.0867691i
$705$		0			0
$706$	−6.34826e27	−	1.09955e28i	−0.206352	−	0.357411i
$707$	−4.72547e27	+	2.72825e27i	−0.151444	+	0.0874360i
$708$		0			0
$709$	3.59242e27	−	6.22225e27i	0.111924	−	0.193859i	−0.804622	−	0.593788i	$-0.797632\pi$
$709$	3.59242e27	−	6.22225e27i	0.111924	−	0.193859i	0.916546	+	0.399929i	$0.130965\pi$
$710$			1.59171e28i			0.488969i
$711$		0			0
$712$	1.90667e28			0.569477
$713$	−1.11681e28	−	6.44788e27i	−0.328914	−	0.189899i
$714$		0			0
$715$	−1.34591e28	−	2.33119e28i	−0.385440	−	0.667602i
$716$	2.23674e28	−	1.29138e28i	0.631663	−	0.364691i
$717$		0			0
$718$	1.97690e28	−	3.42409e28i	0.542925	−	0.940374i
$719$			5.39954e28i			1.46240i	0.682161	+	0.731202i	$0.261040\pi$
$719$			5.39954e28i			1.46240i	−0.682161	+	0.731202i	$0.738960\pi$
$720$		0			0
$721$	9.04749e27			0.238328
$722$	−2.32846e28	−	1.34434e28i	−0.604919	−	0.349250i
$723$		0			0
$724$	1.38555e28	+	2.39984e28i	0.350135	+	0.606451i
$725$	−2.04977e28	+	1.18344e28i	−0.510888	+	0.294961i
$726$		0			0
$727$	−3.76699e28	+	6.52462e28i	−0.913378	+	1.58202i	−0.104120	+	0.994565i	$0.533203\pi$
$727$	−3.76699e28	+	6.52462e28i	−0.913378	+	1.58202i	−0.809258	+	0.587453i	$0.800131\pi$
$728$		−	1.43424e28i		−	0.343011i
$729$		0			0
$730$	3.47421e28			0.808403
$731$	−7.43760e28	−	4.29410e28i	−1.70710	−	0.985595i
$732$		0			0
$733$	−1.16755e28	−	2.02226e28i	−0.260758	−	0.451645i	0.705686	−	0.708525i	$-0.250639\pi$
$733$	−1.16755e28	−	2.02226e28i	−0.260758	−	0.451645i	−0.966443	+	0.256880i	$0.917306\pi$
$734$	−6.10470e27	+	3.52455e27i	−0.134494	+	0.0776504i
$735$		0			0
$736$	−4.41455e27	+	7.64623e27i	−0.0946474	+	0.163934i
$737$		−	1.19536e29i		−	2.52826i
$738$		0			0
$739$	1.10513e28			0.227494			0.113747	−	0.993510i	$-0.463715\pi$
$739$	1.10513e28			0.227494			0.113747	+	0.993510i	$0.463715\pi$
$740$	−1.14931e28	−	6.63554e27i	−0.233410	−	0.134759i
$741$		0			0
$742$	−1.69395e28	−	2.93402e28i	−0.334860	−	0.579994i
$743$	−3.65996e28	+	2.11308e28i	−0.713820	+	0.412124i	−0.812474	−	0.582998i	$-0.801880\pi$
$743$	−3.65996e28	+	2.11308e28i	−0.713820	+	0.412124i	0.0986540	+	0.995122i	$0.468546\pi$
$744$		0			0
$745$	9.98156e27	−	1.72886e28i	0.189511	−	0.328244i
$746$			6.70367e28i			1.25581i
$747$		0			0
$748$	7.45536e28			1.35973
$749$	1.24875e27	+	7.20966e26i	0.0224728	+	0.0129747i
$750$		0			0
$751$	−2.91773e28	−	5.05365e28i	−0.511264	−	0.885536i	−0.999915	−	0.0130561i	$-0.995844\pi$
$751$	−2.91773e28	−	5.05365e28i	−0.511264	−	0.885536i	0.488650	−	0.872480i	$-0.337489\pi$
$752$	1.62899e28	−	9.40499e27i	0.281670	−	0.162622i
$753$		0			0
$754$	1.93037e28	−	3.34350e28i	0.325032	−	0.562973i
$755$		−	3.78192e28i		−	0.628409i
$756$		0			0
$757$	6.36147e28			1.02943			0.514717	−	0.857360i	$-0.327897\pi$
$757$	6.36147e28			1.02943			0.514717	+	0.857360i	$0.327897\pi$
$758$	3.95603e27	+	2.28402e27i	0.0631783	+	0.0364760i
$759$		0			0
$760$	−8.79518e26	−	1.52337e27i	−0.0136807	−	0.0236957i
$761$	9.02875e28	−	5.21275e28i	1.38606	−	0.800240i	0.393189	−	0.919458i	$-0.371372\pi$
$761$	9.02875e28	−	5.21275e28i	1.38606	−	0.800240i	0.992868	+	0.119217i	$0.0380385\pi$
$762$		0			0
$763$	7.07539e28	−	1.22549e29i	1.05805	−	1.83259i
$764$		−	1.20786e28i		−	0.178272i
$765$		0			0
$766$	1.58059e28			0.227265
$767$	7.07805e28	+	4.08652e28i	1.00452	+	0.579962i
$768$		0			0
$769$	−1.08779e28	−	1.88410e28i	−0.150411	−	0.260520i	0.780967	−	0.624572i	$-0.214726\pi$
$769$	−1.08779e28	−	1.88410e28i	−0.150411	−	0.260520i	−0.931379	+	0.364052i	$0.881393\pi$
$770$	5.35513e28	−	3.09179e28i	0.730908	−	0.421990i
$771$		0			0
$772$	1.10539e28	−	1.91459e28i	0.147009	−	0.254627i
$773$		−	5.75380e26i		−	0.00755370i	−0.999993	−	0.00377685i	$-0.998798\pi$
$773$		−	5.75380e26i		−	0.00755370i	0.999993	−	0.00377685i	$-0.00120221\pi$
$774$		0			0
$775$	1.40824e28			0.180160
$776$	3.48563e27	+	2.01243e27i	0.0440214	+	0.0254158i
$777$		0			0
$778$	−3.10269e27	−	5.37402e27i	−0.0381894	−	0.0661459i
$779$	6.75113e27	−	3.89777e27i	0.0820355	−	0.0473632i
$780$		0			0
$781$	−5.77772e28	+	1.00073e29i	−0.684299	+	1.18524i
$782$		−	1.26842e29i		−	1.48319i
$783$		0			0
$784$	1.10138e28			0.125538
$785$	−3.46746e28	−	2.00194e28i	−0.390224	−	0.225296i
$786$		0			0
$787$	−2.61109e28	−	4.52254e28i	−0.286467	−	0.496175i	0.686497	−	0.727133i	$-0.259148\pi$
$787$	−2.61109e28	−	4.52254e28i	−0.286467	−	0.496175i	−0.972964	+	0.230957i	$0.925814\pi$
$788$	1.66673e28	−	9.62286e27i	0.180552	−	0.104242i
$789$		0			0
$790$	−1.31989e28	+	2.28612e28i	−0.139402	+	0.241451i
$791$		−	1.31291e29i		−	1.36921i
$792$		0			0
$793$	4.80737e28			0.488850
$794$	−6.62950e28	−	3.82754e28i	−0.665696	−	0.384340i
$795$		0			0
$796$	−3.20151e27	−	5.54518e27i	−0.0313491	−	0.0542982i
$797$	−3.98687e28	+	2.30182e28i	−0.385522	+	0.222581i	−0.680218	−	0.733010i	$-0.738115\pi$
$797$	−3.98687e28	+	2.30182e28i	−0.385522	+	0.222581i	0.294696	+	0.955591i	$0.404782\pi$
$798$		0			0
$799$	−1.35115e29	+	2.34027e29i	−1.27420	+	2.20698i
$800$		−	9.64151e27i		−	0.0897936i
$801$		0			0
$802$	−1.49425e29			−1.35731
$803$	2.18428e29	+	1.26110e29i	1.95954	+	1.13134i
$804$		0			0
$805$	−5.26022e28	−	9.11097e28i	−0.460305	−	0.797271i
$806$	−1.98930e28	+	1.14852e28i	−0.171930	+	0.0992636i
$807$		0			0
$808$	2.99159e27	−	5.18158e27i	0.0252225	−	0.0436867i
$809$			8.24121e28i			0.686287i	0.939283	+	0.343143i	$0.111492\pi$
$809$			8.24121e28i			0.686287i	−0.939283	+	0.343143i	$0.888508\pi$
$810$		0			0
$811$	1.92459e29			1.56361			0.781805	−	0.623522i	$-0.214299\pi$
$811$	1.92459e29			1.56361			0.781805	+	0.623522i	$0.214299\pi$
$812$	7.68056e28	+	4.43437e28i	0.616357	+	0.355854i
$813$		0			0
$814$	−4.81724e28	−	8.34370e28i	−0.377185	−	0.653303i
$815$	−2.90985e28	+	1.68001e28i	−0.225058	+	0.129938i
$816$		0			0
$817$	−7.35530e27	+	1.27398e28i	−0.0555111	+	0.0961481i
$818$			1.73548e29i			1.29386i
$819$		0			0
$820$	−4.13910e28			−0.301139
$821$	−9.72425e28	−	5.61430e28i	−0.698915	−	0.403519i	0.108028	−	0.994148i	$-0.465546\pi$
$821$	−9.72425e28	−	5.61430e28i	−0.698915	−	0.403519i	−0.806943	+	0.590629i	$0.798880\pi$
$822$		0			0
$823$	−1.00668e28	−	1.74362e28i	−0.0706144	−	0.122308i	0.828556	−	0.559906i	$-0.189163\pi$
$823$	−1.00668e28	−	1.74362e28i	−0.0706144	−	0.122308i	−0.899171	+	0.437598i	$0.855829\pi$
$824$	−8.59165e27	+	4.96039e27i	−0.0595394	+	0.0343751i
$825$		0			0
$826$	−9.38740e28	+	1.62595e29i	−0.634958	+	1.09978i
$827$		−	1.27346e29i		−	0.851000i	−0.904958	−	0.425500i	$-0.860098\pi$
$827$		−	1.27346e29i		−	0.851000i	0.904958	−	0.425500i	$-0.139902\pi$
$828$		0			0
$829$	−8.05711e28			−0.525574			−0.262787	−	0.964854i	$-0.584642\pi$
$829$	−8.05711e28			−0.525574			−0.262787	+	0.964854i	$0.584642\pi$
$830$	−1.89898e28	−	1.09638e28i	−0.122388	−	0.0706609i
$831$		0			0
$832$	7.86339e27	+	1.36198e28i	0.0494740	+	0.0856914i
$833$	−1.37029e29	+	7.91138e28i	−0.851850	+	0.491816i
$834$		0			0
$835$	9.54991e28	−	1.65409e29i	0.579608	−	1.00391i
$836$		−	1.27702e28i		−	0.0765833i
$837$		0			0
$838$	8.95605e28			0.524416
$839$	−4.52553e28	−	2.61282e28i	−0.261848	−	0.151178i	0.363329	−	0.931661i	$-0.381640\pi$
$839$	−4.52553e28	−	2.61282e28i	−0.261848	−	0.151178i	−0.625177	+	0.780483i	$0.714973\pi$
$840$		0			0
$841$	3.08686e28	+	5.34659e28i	0.174404	+	0.302077i
$842$	−1.37406e29	+	7.93315e28i	−0.767159	+	0.442920i
$843$		0			0
$844$	−2.96459e28	+	5.13483e28i	−0.161637	+	0.279963i
$845$		−	4.86118e28i		−	0.261923i
$846$		0			0
$847$	2.16000e29			1.13663
$848$	3.21721e28	+	1.85746e28i	0.167310	+	0.0965964i
$849$		0			0
$850$	6.92567e28	+	1.19956e29i	0.351781	+	0.609303i
$851$	−1.41956e29	+	8.19583e28i	−0.712620	+	0.411431i
$852$		0			0
$853$	−3.12309e28	+	5.40936e28i	−0.153142	+	0.265250i	−0.932381	−	0.361477i	$-0.882273\pi$
$853$	−3.12309e28	+	5.40936e28i	−0.153142	+	0.265250i	0.779239	+	0.626727i	$0.215606\pi$
$854$			1.10433e29i			0.535206i
$855$		0			0
$856$	−1.58111e27			−0.00748557
$857$	1.55842e29	+	8.99753e28i	0.729249	+	0.421032i	0.818147	−	0.575009i	$-0.195001\pi$
$857$	1.55842e29	+	8.99753e28i	0.729249	+	0.421032i	−0.0888984	+	0.996041i	$0.528335\pi$
$858$		0			0
$859$	−4.73984e27	−	8.20964e27i	−0.0216687	−	0.0375312i	0.854988	−	0.518648i	$-0.173565\pi$
$859$	−4.73984e27	−	8.20964e27i	−0.0216687	−	0.0375312i	−0.876656	+	0.481117i	$0.840231\pi$
$860$	6.76428e28	−	3.90536e28i	0.305659	−	0.176472i
$861$		0			0
$862$	4.85910e28	−	8.41621e28i	0.214528	−	0.371573i
$863$			3.07896e29i			1.34368i	0.740696	+	0.671841i	$0.234496\pi$
$863$			3.07896e29i			1.34368i	−0.740696	+	0.671841i	$0.765504\pi$
$864$		0			0
$865$	1.20506e28			0.0513865
$866$	−4.71632e28	−	2.72297e28i	−0.198804	−	0.114779i
$867$		0			0
$868$	−2.63835e28	−	4.56976e28i	−0.108676	−	0.188233i
$869$	−1.65967e29	+	9.58210e28i	−0.675808	+	0.390178i
$870$		0			0
$871$	−1.81128e29	+	3.13723e29i	−0.720782	+	1.24843i
$872$			1.55166e29i			0.610426i
$873$		0			0
$874$	−2.17266e28			−0.0835367
$875$	2.95366e29	+	1.70529e29i	1.12274	+	0.648214i
$876$		0			0
$877$	6.19063e28	+	1.07225e29i	0.230006	+	0.398382i	0.957810	−	0.287404i	$-0.0927921\pi$
$877$	6.19063e28	+	1.07225e29i	0.230006	+	0.398382i	−0.727804	+	0.685786i	$0.759459\pi$
$878$	−9.29961e28	+	5.36913e28i	−0.341601	+	0.197224i
$879$		0			0
$880$	−3.39021e28	+	5.87202e28i	−0.121731	+	0.210844i
$881$			1.84569e29i			0.655238i	0.944810	+	0.327619i	$0.106246\pi$
$881$			1.84569e29i			0.655238i	−0.944810	+	0.327619i	$0.893754\pi$
$882$		0			0
$883$	−3.66084e29			−1.27050			−0.635249	−	0.772307i	$-0.719103\pi$
$883$	−3.66084e29			−1.27050			−0.635249	+	0.772307i	$0.719103\pi$
$884$	−1.95667e29	−	1.12968e29i	−0.671421	−	0.387645i
$885$		0			0
$886$	−1.20983e28	−	2.09549e28i	−0.0405871	−	0.0702989i
$887$	−9.06355e28	+	5.23284e28i	−0.300651	+	0.173581i	−0.642735	−	0.766088i	$-0.722200\pi$
$887$	−9.06355e28	+	5.23284e28i	−0.300651	+	0.173581i	0.342084	+	0.939669i	$0.388867\pi$
$888$		0			0
$889$	2.46166e29	−	4.26372e29i	0.798381	−	1.38284i
$890$		−	2.49122e29i		−	0.798935i
$891$		0			0
$892$	−9.88729e28			−0.310048
$893$	4.00861e28	+	2.31437e28i	0.124302	+	0.0717660i
$894$		0			0
$895$	−1.68729e29	−	2.92247e29i	−0.511634	−	0.886177i
$896$	−3.12869e28	+	1.80635e28i	−0.0938172	+	0.0541654i
$897$		0			0
$898$	−2.29777e29	+	3.97986e29i	−0.673819	+	1.16709i
$899$		−	1.42040e29i		−	0.411921i
$900$		0			0
$901$	−5.33699e29			−1.51373
$902$	−2.60231e29	−	1.50244e29i	−0.729950	−	0.421437i
$903$		0			0
$904$	7.19817e28	+	1.24676e29i	0.197487	+	0.342057i
$905$	3.13557e29	−	1.81032e29i	0.850807	−	0.491213i
$906$		0			0
$907$	−1.11435e29	+	1.93010e29i	−0.295765	+	0.512281i	−0.975163	−	0.221490i	$-0.928908\pi$
$907$	−1.11435e29	+	1.93010e29i	−0.295765	+	0.512281i	0.679397	+	0.733771i	$0.262241\pi$
$908$			1.01583e29i			0.266664i
$909$		0			0
$910$	−1.87395e29			−0.481220
$911$	1.00163e29	+	5.78293e28i	0.254405	+	0.146881i	0.621779	−	0.783192i	$-0.286410\pi$
$911$	1.00163e29	+	5.78293e28i	0.254405	+	0.146881i	−0.367375	+	0.930073i	$0.619743\pi$
$912$		0			0
$913$	−7.95943e28	−	1.37861e29i	−0.197776	−	0.342559i
$914$	2.81417e29	−	1.62476e29i	0.691653	−	0.399326i
$915$		0			0
$916$	−1.24661e29	+	2.15919e29i	−0.299762	+	0.519203i
$917$			4.05449e29i			0.964368i
$918$		0			0
$919$	8.25764e29			1.92177			0.960883	−	0.276954i	$-0.0893248\pi$
$919$	8.25764e29			1.92177			0.960883	+	0.276954i	$0.0893248\pi$
$920$	9.99039e28	+	5.76795e28i	0.229987	+	0.132783i
$921$		0			0
$922$	5.13454e28	+	8.89329e28i	0.115662	+	0.200333i
$923$	3.03274e29	−	1.75095e29i	0.675800	−	0.390173i
$924$		0			0
$925$	8.94996e28	−	1.55018e29i	0.195166	−	0.338037i
$926$			5.42765e29i			1.17085i
$927$		0			0
$928$	−9.72478e28			−0.205305
$929$	5.08109e29	+	2.93357e29i	1.06121	+	0.612687i	0.925765	−	0.378098i	$-0.123422\pi$
$929$	5.08109e29	+	2.93357e29i	1.06121	+	0.612687i	0.135440	+	0.990786i	$0.456755\pi$
$930$		0			0
$931$	1.35513e28	+	2.34715e28i	0.0277003	+	0.0479783i
$932$	−5.97784e28	+	3.45131e28i	−0.120889	+	0.0697951i
$933$		0			0
$934$	−1.33901e29	+	2.31923e29i	−0.265041	+	0.459065i
$935$		−	9.74100e29i		−	1.90760i
$936$		0			0
$937$	−2.58444e28			−0.0495416			−0.0247708	−	0.999693i	$-0.507886\pi$
$937$	−2.58444e28			−0.0495416			−0.0247708	+	0.999693i	$0.507886\pi$
$938$	−7.20673e29	−	4.16081e29i	−1.36682	−	0.789131i
$939$		0			0
$940$	−1.22883e29	−	2.12840e29i	−0.228147	−	0.395162i
$941$	5.46385e29	−	3.15456e29i	1.00370	−	0.579485i	0.0943573	−	0.995538i	$-0.469920\pi$
$941$	5.46385e29	−	3.15456e29i	1.00370	−	0.579485i	0.909340	+	0.416053i	$0.136587\pi$
$942$		0			0
$943$	−2.55619e29	+	4.42745e29i	−0.459701	+	0.796226i
$944$		−	2.05870e29i		−	0.366330i
$945$		0			0
$946$	5.67039e29			0.987873
$947$	3.26875e29	+	1.88721e29i	0.563484	+	0.325328i	0.754543	−	0.656251i	$-0.227859\pi$
$947$	3.26875e29	+	1.88721e29i	0.563484	+	0.325328i	−0.191058	+	0.981579i	$0.561192\pi$
$948$		0			0
$949$	−3.82179e29	−	6.61953e29i	−0.645066	−	1.11729i
$950$	2.05471e28	−	1.18629e28i	0.0343174	−	0.0198132i
$951$		0			0
$952$	2.59507e29	−	4.49479e29i	0.424404	−	0.735089i
$953$		−	4.14984e29i		−	0.671588i	−0.941935	−	0.335794i	$-0.890995\pi$
$953$		−	4.14984e29i		−	0.671588i	0.941935	−	0.335794i	$-0.109005\pi$
$954$		0			0
$955$	−1.57817e29			−0.250103
$956$	−4.16710e29	−	2.40588e29i	−0.653514	−	0.377307i
$957$		0			0
$958$	−1.84713e29	−	3.19932e29i	−0.283688	−	0.491363i
$959$	−1.10728e29	+	6.39287e28i	−0.168295	+	0.0971649i
$960$		0			0
$961$	2.93640e29	−	5.08599e29i	0.437101	−	0.757080i
$962$			2.91975e29i			0.430126i
$963$		0			0
$964$	2.06701e29			0.298245
$965$	−2.50157e29	−	1.44428e29i	−0.357223	−	0.206243i
$966$		0			0
$967$	5.00708e28	+	8.67252e28i	0.0700358	+	0.121306i	0.898917	−	0.438119i	$-0.144355\pi$
$967$	5.00708e28	+	8.67252e28i	0.0700358	+	0.121306i	−0.828881	+	0.559425i	$0.811022\pi$
$968$	−2.05118e29	+	1.18425e29i	−0.283955	+	0.163941i
$969$		0			0
$970$	2.62939e28	−	4.55424e28i	0.0356565	−	0.0617588i
$971$			2.57696e29i			0.345872i	0.984933	+	0.172936i	$0.0553254\pi$
$971$			2.57696e29i			0.345872i	−0.984933	+	0.172936i	$0.944675\pi$
$972$		0			0
$973$	1.62010e29			0.213017
$974$	−2.67106e29	−	1.54213e29i	−0.347611	−	0.200693i
$975$		0			0
$976$	−6.05463e28	−	1.04869e29i	−0.0771950	−	0.133706i
$977$	−3.16209e29	+	1.82563e29i	−0.399051	+	0.230392i	−0.686075	−	0.727531i	$-0.740668\pi$
$977$	−3.16209e29	+	1.82563e29i	−0.399051	+	0.230392i	0.287023	+	0.957924i	$0.407334\pi$
$978$		0			0
$979$	9.04281e29	−	1.56626e30i	1.11809	−	1.93659i
$980$		−	1.43903e29i		−	0.176121i
$981$		0			0
$982$	6.34395e29			0.760755
$983$	−5.50252e29	−	3.17688e29i	−0.653171	−	0.377108i	0.136499	−	0.990640i	$-0.456415\pi$
$983$	−5.50252e29	−	3.17688e29i	−0.653171	−	0.377108i	−0.789670	+	0.613532i	$0.789748\pi$
$984$		0			0
$985$	−1.25730e29	−	2.17771e29i	−0.146244	−	0.253301i
$986$	1.20992e30	−	6.98549e29i	1.39312	−	0.804318i
$987$		0			0
$988$	−1.93502e28	+	3.35155e28i	−0.0218331	+	0.0378160i
$989$		−	9.64734e29i		−	1.07757i
$990$		0			0
$991$	4.90773e29			0.537210			0.268605	−	0.963250i	$-0.413437\pi$
$991$	4.90773e29			0.537210			0.268605	+	0.963250i	$0.413437\pi$
$992$	5.01084e28	+	2.89301e28i	0.0542993	+	0.0313497i
$993$		0			0
$994$	4.02223e29	+	6.96670e29i	0.427172	+	0.739884i
$995$	−7.24521e28	+	4.18302e28i	−0.0761764	+	0.0439804i
$996$		0			0
$997$	−3.82823e29	+	6.63069e29i	−0.394500	+	0.683293i	−0.993037	−	0.117801i	$-0.962415\pi$
$997$	−3.82823e29	+	6.63069e29i	−0.394500	+	0.683293i	0.598538	+	0.801095i	$0.295749\pi$
$998$			1.35214e30i			1.37948i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.21.d.a.35.16		40
3.2	odd	2		18.21.d.a.11.5	yes	40
9.4	even	3		18.21.d.a.5.5	✓	40
9.5	odd	6	inner	54.21.d.a.17.16		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.21.d.a.5.5	✓	40	9.4	even	3
18.21.d.a.11.5	yes	40	3.2	odd	2
54.21.d.a.17.16		40	9.5	odd	6	inner
54.21.d.a.35.16		40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	54.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(627.069 + 362.039i) q^{2} +(262144. + 454047. i) q^{4} +(5.93247e6 - 3.42511e6i) q^{5} +(1.73104e8 - 2.99825e8i) q^{7} +3.79625e8i q^{8} +4.96010e9 q^{10} +(3.11848e10 + 1.80045e10i) q^{11} +(-5.45632e10 - 9.45063e10i) q^{13} +(2.17097e11 - 1.25341e11i) q^{14} +(-1.37439e11 + 2.38051e11i) q^{16} -3.94900e12i q^{17} -6.76417e11 q^{19} +(3.11032e12 + 1.79575e12i) q^{20} +(1.30367e13 + 2.25802e13i) q^{22} +(3.84169e13 - 2.21800e13i) q^{23} +(-2.42209e13 + 4.19518e13i) q^{25} -7.90160e13i q^{26} +1.81513e14 q^{28} +(4.23142e14 + 2.44301e14i) q^{29} +(-1.45353e14 - 2.51760e14i) q^{31} +(-1.72368e14 + 9.95164e13i) q^{32} +(1.42969e15 - 2.47629e15i) q^{34} -2.37161e15i q^{35} -3.69514e15 q^{37} +(-4.24161e14 - 2.44889e14i) q^{38} +(1.30026e15 + 2.25212e15i) q^{40} +(-9.98071e15 + 5.76237e15i) q^{41} +(1.08739e16 - 1.88342e16i) q^{43} +1.88791e16i q^{44} +3.21201e16 q^{46} +(-5.92624e16 - 3.42152e16i) q^{47} +(-2.00339e16 - 3.46998e16i) q^{49} +(-3.03764e16 + 1.75378e16i) q^{50} +(2.86069e16 - 4.95485e16i) q^{52} -1.35148e17i q^{53} +2.46670e17 q^{55} +(1.13821e17 + 6.57146e16i) q^{56} +(1.76893e17 + 3.06387e17i) q^{58} +(-6.48610e17 + 3.74475e17i) q^{59} +(-2.20266e17 + 3.81512e17i) q^{61} -2.10494e17i q^{62} -1.44115e17 q^{64} +(-6.47390e17 - 3.73771e17i) q^{65} +(-1.65980e18 - 2.87486e18i) q^{67} +(1.79303e18 - 1.03521e18i) q^{68} +(8.58613e17 - 1.48716e18i) q^{70} +3.20903e18i q^{71} +7.00433e18 q^{73} +(-2.31711e18 - 1.33778e18i) q^{74} +(-1.77319e17 - 3.07125e17i) q^{76} +(1.07964e19 - 6.23332e18i) q^{77} +(-2.66102e18 + 4.60903e18i) q^{79} +1.88298e18i q^{80} -8.34480e18 q^{82} +(-3.82852e18 - 2.21040e18i) q^{83} +(-1.35258e19 - 2.34273e19i) q^{85} +(1.36374e19 - 7.87355e18i) q^{86} +(-6.83497e18 + 1.18385e19i) q^{88} -5.02252e19i q^{89} -3.77805e19 q^{91} +(2.01415e19 + 1.16287e19i) q^{92} +(-2.47744e19 - 4.29105e19i) q^{94} +(-4.01283e18 + 2.31681e18i) q^{95} +(5.30109e18 - 9.18176e18i) q^{97} -2.90122e19i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10485760 q^{4} - 29763918 q^{5} + 133479866 q^{7} + 35793208728 q^{11} + 39827158550 q^{13} - 187564400640 q^{14} - 5497558138880 q^{16} - 10560819523540 q^{19} - 15604865040384 q^{20} + 10829007458304 q^{22}+ \cdots - 66\!\cdots\!16 q^{97}+O(q^{100}) \) 40 * q + 10485760 * q^4 - 29763918 * q^5 + 133479866 * q^7 + 35793208728 * q^11 + 39827158550 * q^13 - 187564400640 * q^14 - 5497558138880 * q^16 - 10560819523540 * q^19 - 15604865040384 * q^20 + 10829007458304 * q^22 + 95164852839678 * q^23 + 485893942617694 * q^25 + 139963783970816 * q^28 - 487337329131246 * q^29 - 386065992062842 * q^31 - 810410730184704 * q^34 + 7650497672534432 * q^37 + 27431157167935488 * q^38 + 76546903885431012 * q^41 - 10868849409851092 * q^43 + 13732137981788160 * q^46 - 220882065588142506 * q^47 - 201918836583922386 * q^49 - 84434006357065728 * q^50 - 20880901301862400 * q^52 - 689556443803109316 * q^55 - 98337764482744320 * q^56 + 289875600503808000 * q^58 + 4671324023815652220 * q^59 - 608513692992272866 * q^61 - 5764607523034234880 * q^64 - 4959300225343873626 * q^65 - 2581864509390888904 * q^67 + 5171455594224156672 * q^68 - 584784912675889152 * q^70 + 15022099327729072004 * q^73 - 7089371473773993984 * q^74 - 2768455473178869760 * q^76 + 30865724759591472834 * q^77 + 18532232803602736754 * q^79 - 35601230743051272192 * q^82 - 54829678294093455594 * q^83 + 43688870161052471388 * q^85 - 47393791396458614784 * q^86 - 5677518662299287552 * q^88 - 35182774173576758996 * q^91 + 49893790365609099264 * q^92 + 19892618446780047360 * q^94 - 332020921293200455200 * q^95 - 66463398176406835216 * q^97

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